Search for the decay η0
M. Ablikim,1M. N. Achasov,10,dP. Adlarson,59S. Ahmed,15M. Albrecht,4M. Alekseev,58a,58cA. Amoroso,58a,58cF. F. An,1 Q. An,55,43Y. Bai,42O. Bakina,27R. Baldini Ferroli,23aI. Balossino,24aY. Ban,35K. Begzsuren,25J. V. Bennett,5N. Berger,26 M. Bertani,23aD. Bettoni,24a F. Bianchi,58a,58c J. Biernat,59J. Bloms,52I. Boyko,27R. A. Briere,5 H. Cai,60X. Cai,1,43 A. Calcaterra,23aG. F. Cao,1,47N. Cao,1,47S. A. Cetin,46b J. Chai,58c J. F. Chang,1,43W. L. Chang,1,47G. Chelkov,27,b,c
D. Y. Chen,6 G. Chen,1H. S. Chen,1,47J. C. Chen,1 M. L. Chen,1,43S. J. Chen,33Y. B. Chen,1,43W. Cheng,58c G. Cibinetto,24aF. Cossio,58cX. F. Cui,34H. L. Dai,1,43J. P. Dai,38,hX. C. Dai,1,47A. Dbeyssi,15D. Dedovich,27Z. Y. Deng,1
A. Denig,26I. Denysenko,27 M. Destefanis,58a,58c F. De Mori,58a,58c Y. Ding,31C. Dong,34 J. Dong,1,43L. Y. Dong,1,47 M. Y. Dong,1,43,47Z. L. Dou,33S. X. Du,63J. Z. Fan,45J. Fang,1,43S. S. Fang,1,47Y. Fang,1R. Farinelli,24a,24bL. Fava,58b,58c F. Feldbauer,4G. Felici,23a C. Q. Feng,55,43M. Fritsch,4 C. D. Fu,1Y. Fu,1 Q. Gao,1 X. L. Gao,55,43Y. Gao,56Y. Gao,45
Y. G. Gao,6Z. Gao,55,43 B. Garillon,26I. Garzia,24a E. M. Gersabeck,50 A. Gilman,51K. Goetzen,11L. Gong,34 W. X. Gong,1,43W. Gradl,26M. Greco,58a,58c L. M. Gu,33M. H. Gu,1,43S. Gu,2 Y. T. Gu,13A. Q. Guo,22L. B. Guo,32
R. P. Guo,36Y. P. Guo,26A. Guskov,27S. Han,60X. Q. Hao,16 F. A. Harris,48 K. L. He,1,47F. H. Heinsius,4 T. Held,4 Y. K. Heng,1,43,47M. Himmelreich,11,gY. R. Hou,47Z. L. Hou,1 H. M. Hu,1,47J. F. Hu,38,hT. Hu,1,43,47 Y. Hu,1 G. S. Huang,55,43 J. S. Huang,16 X. T. Huang,37 X. Z. Huang,33 N. Huesken,52T. Hussain,57W. Ikegami Andersson,59
W. Imoehl,22M. Irshad,55,43 Q. Ji,1Q. P. Ji,16 X. B. Ji,1,47X. L. Ji,1,43H. L. Jiang,37X. S. Jiang,1,43,47 X. Y. Jiang,34 J. B. Jiao,37Z. Jiao,18D. P. Jin,1,43,47 S. Jin,33Y. Jin,49T. Johansson,59N. Kalantar-Nayestanaki,29X. S. Kang,31 R. Kappert,29M. Kavatsyuk,29B. C. Ke,1 I. K. Keshk,4 A. Khoukaz,52P. Kiese,26R. Kiuchi,1 R. Kliemt,11 L. Koch,28 O. B. Kolcu,46b,fB. Kopf,4M. Kuemmel,4M. Kuessner,4A. Kupsc,59M. Kurth,1M. G. Kurth,1,47W. Kühn,28J. S. Lange,28 P. Larin,15L. Lavezzi,58cH. Leithoff,26T. Lenz,26C. Li,59Cheng Li,55,43D. M. Li,63F. Li,1,43F. Y. Li,35G. Li,1H. B. Li,1,47 H. J. Li,9,jJ. C. Li,1J. W. Li,41Ke Li,1 L. K. Li,1 Lei Li,3P. L. Li,55,43 P. R. Li,30Q. Y. Li,37W. D. Li,1,47W. G. Li,1
X. H. Li,55,43X. L. Li,37X. N. Li,1,43Z. B. Li,44Z. Y. Li,44H. Liang,55,43 H. Liang,1,47Y. F. Liang,40Y. T. Liang,28 G. R. Liao,12L. Z. Liao,1,47J. Libby,21C. X. Lin,44D. X. Lin,15Y. J. Lin,13B. Liu,38,hB. J. Liu,1C. X. Liu,1D. Liu,55,43 D. Y. Liu,38,h F. H. Liu,39Fang Liu,1 Feng Liu,6H. B. Liu,13H. M. Liu,1,47Huanhuan Liu,1 Huihui Liu,17J. B. Liu,55,43 J. Y. Liu,1,47K. Y. Liu,31Ke Liu,6 L. Y. Liu,13Q. Liu,47 S. B. Liu,55,43T. Liu,1,47X. Liu,30X. Y. Liu,1,47Y. B. Liu,34 Z. A. Liu,1,43,47Zhiqing Liu,37Y. F. Long,35X. C. Lou,1,43,47H. J. Lu,18J. D. Lu,1,47J. G. Lu,1,43Y. Lu,1 Y. P. Lu,1,43 C. L. Luo,32M. X. Luo,62P. W. Luo,44T. Luo,9,jX. L. Luo,1,43S. Lusso,58cX. R. Lyu,47F. C. Ma,31H. L. Ma,1L. L. Ma,37
M. M. Ma,1,47Q. M. Ma,1 X. N. Ma,34 X. X. Ma,1,47X. Y. Ma,1,43Y. M. Ma,37F. E. Maas,15M. Maggiora,58a,58c S. Maldaner,26S. Malde,53Q. A. Malik,57A. Mangoni,23b Y. J. Mao,35Z. P. Mao,1 S. Marcello,58a,58c Z. X. Meng,49
J. G. Messchendorp,29G. Mezzadri,24a J. Min,1,43 T. J. Min,33R. E. Mitchell,22 X. H. Mo,1,43,47 Y. J. Mo,6 C. Morales Morales,15N. Yu. Muchnoi,10,dH. Muramatsu,51A. Mustafa,4 S. Nakhoul,11,gY. Nefedov,27F. Nerling,11,g
I. B. Nikolaev,10,d Z. Ning,1,43S. Nisar,8,k S. L. Niu,1,43S. L. Olsen,47Q. Ouyang,1,43,47 S. Pacetti,23bY. Pan,55,43 M. Papenbrock,59P. Patteri,23a M. Pelizaeus,4H. P. Peng,55,43 K. Peters,11,g J. Pettersson,59J. L. Ping,32R. G. Ping,1,47 A. Pitka,4R. Poling,51V. Prasad,55,43H. R. Qi,2M. Qi,33T. Y. Qi,2S. Qian,1,43C. F. Qiao,47N. Qin,60X. P. Qin,13X. S. Qin,4 Z. H. Qin,1,43J. F. Qiu,1S. Q. Qu,34K. H. Rashid,57,iK. Ravindran,21C. F. Redmer,26M. Richter,4A. Rivetti,58cV. Rodin,29 M. Rolo,58c G. Rong,1,47Ch. Rosner,15 M. Rump,52A. Sarantsev,27,e M. Savri´e,24b Y. Schelhaas,26K. Schoenning,59 W. Shan,19X. Y. Shan,55,43M. Shao,55,43C. P. Shen,2P. X. Shen,34X. Y. Shen,1,47H. Y. Sheng,1X. Shi,1,43X. D. Shi,55,43 J. J. Song,37Q. Q. Song,55,43 X. Y. Song,1S. Sosio,58a,58cC. Sowa,4S. Spataro,58a,58cF. F. Sui,37G. X. Sun,1J. F. Sun,16
L. Sun,60S. S. Sun,1,47 X. H. Sun,1 Y. J. Sun,55,43Y. K. Sun,55,43Y. Z. Sun,1 Z. J. Sun,1,43Z. T. Sun,1 Y. T. Tan,55,43 C. J. Tang,40G. Y. Tang,1 X. Tang,1 V. Thoren,59B. Tsednee,25I. Uman,46d B. Wang,1 B. L. Wang,47 C. W. Wang,33
D. Y. Wang,35K. Wang,1,43L. L. Wang,1 L. S. Wang,1 M. Wang,37M. Z. Wang,35 Meng Wang,1,47P. L. Wang,1 R. M. Wang,61W. P. Wang,55,43 X. Wang,35X. F. Wang,1 X. L. Wang,9,jY. Wang,44Y. Wang,55,43Y. F. Wang,1,43,47 Y. Q. Wang ,1 Z. Wang,1,43Z. G. Wang,1,43Z. Y. Wang,1Zongyuan Wang,1,47T. Weber,4D. H. Wei,12P. Weidenkaff,26 H. W. Wen,32S. P. Wen,1U. Wiedner,4G. Wilkinson,53M. Wolke,59L. H. Wu,1L. J. Wu,1,47Z. Wu,1,43L. Xia,55,43Y. Xia,20 S. Y. Xiao,1Y. J. Xiao,1,47Z. J. Xiao,32Y. G. Xie,1,43Y. H. Xie,6 T. Y. Xing,1,47X. A. Xiong,1,47Q. L. Xiu,1,43G. F. Xu,1 J. J. Xu,33L. Xu,1 Q. J. Xu,14 W. Xu,1,47X. P. Xu,41F. Yan,56L. Yan,58a,58c W. B. Yan,55,43 W. C. Yan,2 Y. H. Yan,20
H. J. Yang,38,hH. X. Yang,1 L. Yang,60R. X. Yang,55,43S. L. Yang,1,47Y. H. Yang,33Y. X. Yang,12Yifan Yang,1,47 Z. Q. Yang,20M. Ye,1,43M. H. Ye,7J. H. Yin,1Z. Y. You,44B. X. Yu,1,43,47C. X. Yu,34J. S. Yu,20T. Yu,56C. Z. Yuan,1,47 X. Q. Yuan,35Y. Yuan,1A. Yuncu,46b,aA. A. Zafar,57Y. Zeng,20B. X. Zhang,1B. Y. Zhang,1,43C. C. Zhang,1D. H. Zhang,1 H. H. Zhang,44H. Y. Zhang,1,43J. Zhang,1,47J. L. Zhang,61J. Q. Zhang,4J. W. Zhang,1,43,47J. Y. Zhang,1J. Z. Zhang,1,47 K. Zhang,1,47L. Zhang,45S. F. Zhang,33T. J. Zhang,38,hX. Y. Zhang,37Y. Zhang,55,43 Y. H. Zhang,1,43 Y. T. Zhang,55,43 Yang Zhang,1Yao Zhang,1Yi Zhang,9,jYu Zhang,47Z. H. Zhang,6Z. P. Zhang,55Z. Y. Zhang,60G. Zhao,1J. W. Zhao,1,43
J. Y. Zhao,1,47J. Z. Zhao,1,43Lei Zhao,55,43Ling Zhao,1M. G. Zhao,34Q. Zhao,1S. J. Zhao,63T. C. Zhao,1Y. B. Zhao,1,43 Z. G. Zhao,55,43 A. Zhemchugov,27,b B. Zheng,56J. P. Zheng,1,43Y. Zheng,35Y. H. Zheng,47B. Zhong,32L. Zhou,1,43 L. P. Zhou,1,47Q. Zhou,1,47X. Zhou,60X. K. Zhou,47X. R. Zhou,55,43Xiaoyu Zhou,20Xu Zhou,20A. N. Zhu,1,47J. Zhu,34
J. Zhu,44K. Zhu,1 K. J. Zhu,1,43,47S. H. Zhu,54W. J. Zhu,34X. L. Zhu,45Y. C. Zhu,55,43 Y. S. Zhu,1,47Z. A. Zhu,1,47 J. Zhuang,1,43B. S. Zou,1 and J. H. Zou1
1Institute of High Energy Physics, Beijing 100049, People’s Republic of China 2
Beihang University, Beijing 100191, People’s Republic of China
3Beijing Institute of Petrochemical Technology, Beijing 102617, People’s Republic of China 4
Bochum Ruhr-University, D-44780 Bochum, Germany
5Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA 6
Central China Normal University, Wuhan 430079, People’s Republic of China
7China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China 8
COMSATS University Islamabad, Lahore Campus, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan
Fudan University, Shanghai 200443, People’s Republic of China
10G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia 11
GSI Helmholtz centre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany
12Guangxi Normal University, Guilin 541004, People’s Republic of China 13
Guangxi University, Nanning 530004, People’s Republic of China
14Hangzhou Normal University, Hangzhou 310036, People’s Republic of China 15
Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany
16Henan Normal University, Xinxiang 453007, People’s Republic of China 17
Henan University of Science and Technology, Luoyang 471003, People’s Republic of China
18Huangshan College, Huangshan 245000, People’s Republic of China 19
Hunan Normal University, Changsha 410081, People’s Republic of China
20Hunan University, Changsha 410082, People’s Republic of China 21
Indian Institute of Technology Madras, Chennai 600036, India
22Indiana University, Bloomington, Indiana 47405, USA 23a
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy
23bINFN and University of Perugia, I-06100 Perugia, Italy 24a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy
24bUniversity of Ferrara, I-44122 Ferrara, Italy 25
Institute of Physics and Technology, Peace Ave. 54B, Ulaanbaatar 13330, Mongolia
26Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany 27
Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
28Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16,
D-35392 Giessen, Germany
29KVI-CART, University of Groningen, NL-9747 AA Groningen, Netherlands 30
Lanzhou University, Lanzhou 730000, People’s Republic of China
31Liaoning University, Shenyang 110036, People’s Republic of China 32
Nanjing Normal University, Nanjing 210023, People’s Republic of China
33Nanjing University, Nanjing 210093, People’s Republic of China 34
Nankai University, Tianjin 300071, People’s Republic of China
35Peking University, Beijing 100871, People’s Republic of China 36
Shandong Normal University, Jinan 250014, People’s Republic of China
37Shandong University, Jinan 250100, People’s Republic of China 38
Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
39Shanxi University, Taiyuan 030006, People’s Republic of China 40
Sichuan University, Chengdu 610064, People’s Republic of China
41Soochow University, Suzhou 215006, People’s Republic of China 42
Southeast University, Nanjing 211100, People’s Republic of China
43State Key Laboratory of Particle Detection and Electronics,
Beijing 100049, Hefei 230026, People’s Republic of China
44Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China 45
Tsinghua University, Beijing 100084, People’s Republic of China
46bIstanbul Bilgi University, 34060 Eyup, Istanbul, Turkey 46c
Uludag University, 16059 Bursa, Turkey
46dNear East University, Nicosia, North Cyprus, Mersin 10, Turkey 47
University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
48University of Hawaii, Honolulu, Hawaii 96822, USA 49
University of Jinan, Jinan 250022, People’s Republic of China
50University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom 51
University of Minnesota, Minneapolis, Minnesota 55455, USA
52University of Muenster, Wilhelm-Klemm-Str. 9, 48149 Muenster, Germany 53
University of Oxford, Keble Rd, Oxford OX13RH, United Kingdom
54University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China 55
University of Science and Technology of China, Hefei 230026, People’s Republic of China
56University of South China, Hengyang 421001, People’s Republic of China 57
University of the Punjab, Lahore-54590, Pakistan
58aUniversity of Turin, I-10125 Turin, Italy 58b
University of Eastern Piedmont, I-15121 Alessandria, Italy
58cINFN, I-10125 Turin, Italy 59
Uppsala University, Box 516, SE-75120 Uppsala, Sweden
60Wuhan University, Wuhan 430072, People’s Republic of China 61
Xinyang Normal University, Xinyang 464000, People’s Republic of China
62Zhejiang University, Hangzhou 310027, People’s Republic of China 63
Zhengzhou University, Zhengzhou 450001, People’s Republic of China (Received 26 June 2019; published 30 September 2019)
Using a data sample of1.31 × 109J=ψ events collected with the BESIII detector, a search for η0→ γγη via J=ψ → γη0is performed for the first time. No significantη0signal is observed in theγγη invariant mass spectrum, and the branching fraction ofη0→ γγη is determined to be less than 1.33 × 10−4 at the 90% confidence level.
The η0 meson provides a unique opportunity for under-standing the distinct symmetry-breaking mechanisms present in low-energy quantum chromodynamics (QCD) [1–5], and its decays play an important role in exploring the effective theory of QCD at low energy . Within the frameworks of the linear σ model and the vector meson dominance (VMD) model[7,8], the branching fractions of η0→ γγπ0andη0→ γγη are predicted to be 3.8 × 10−3and
2.0 × 10−4 , respectively. The dominant contributions
come from the vector meson exchange processes, where for η0→ γγπ0, the ω contributes 80.2% of the total VMD
signal, while theρ contributes 4.6%. For η0→ γγη, ρ and ω contribute 59.9% and 15.8%, respectively.
Recently using1.31 × 109J=ψ events, BESIII reported the study ofη0→ γγπ0for the first time, and the branching fraction ofη0→ γγπ0was determined to beð32.0 0.7 2.3Þ × 10−4 . By excluding the intermediate
con-tributions from ωðρ0Þ → γπ0, the so-called nonresonant branching fraction of η0→ γγπ0 was determined to be ð6.16 0.64 0.67Þ × 10−4 , which confirmed the
theoretical prediction and indicated that this decay was dominated by the VMD processes.
aAlso at Bogazici University, 34342 Istanbul, Turkey. bAlso at the Moscow Institute of Physics and Technology, Moscow 141700, Russia.
cAlso at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russia.
dAlso at the Novosibirsk State University, Novosibirsk, 630090, Russia.
eAlso at the NRC “Kurchatov Institute”, PNPI, 188300, Gatchina, Russia.
fAlso at Istanbul Arel University, 34295 Istanbul, Turkey. gAlso at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany.
hAlso at Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education; Shanghai Key Laboratory for Particle Physics and Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240, People’s Republic of China.
iAlso at Government College Women University, Sialkot— 51310. Punjab, Pakistan.
jAlso at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University, Shanghai 200443, People’s Republic of China.
kAlso at Harvard University, Department of Physics, Cambridge, Massachusetts 02138, USA.
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Unlikeη0→ γγπ0decay, theη0→ γγη decay has not been observed to date. The most stringent upper limit, reported by GAMS-4π setup, on the branching fraction of this decay is 8 × 10−4 at the 90% confidence level (CL) . The BESIII experiment using J=ψ radiative decays has observed a series of η0 new decay modes [11–17], and in this paper we present a search forη0→ γγη in the J=ψ radiative decay.
II. DETECTOR AND MONTE CARLO SIMULATION
The BESIII detector is a magnetic spectrometer  located at the Beijing Electron Position Collider (BEPCII) . The cylindrical core of the BESIII detector consists of a helium-based multilayer drift chamber (MDC), a plastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in a superconducting solenoidal magnet providing a 1.0 T (0.9 T in 2012) magnetic field. The solenoid is supported by an octagonal flux-return yoke with resistive plate counter muon identifier modules interleaved with steel. The acceptance of charged particles and photons is 93% over 4π solid angle. The charged-particle momentum resolution at1 GeV=c is 0.5%, and the dE=dx resolution is 6% for the electrons from Bhabha scattering. The EMC measures photon energies with a resolution of 2.5% (5%) at 1 GeV in the barrel (end cap) region. The time resolution of the TOF barrel part is 68 ps, while that of the end cap part is 110 ps.
Monte Carlo (MC) simulations are used to estimate backgrounds and determine the detection efficiencies. The
GEANT4-based  simulation software BOOST 
includes the geometric and material description of the BESIII detector, detector response, and digitization models, as well as the tracking of the detector running conditions and performance. Production of the charmonium state J=ψ is simulated with KKMC , while the decays are
generated withEVTGENfor known decay modes with
branching fractions taken from the Particle Data Group (PDG)  and by LUNDCHARM  for the remaining unknown decays.
In this analysis, the programEVTGENis used to generate
a J=ψ → γη0 MC sample with an angular distribution of 1 þ cos2θ
γ, where θγ is the polar angle of the radiative
photon in the J=ψ rest frame. The decays η0→ γω (ρ), ωðρÞ → γη are generated using the VMD model[7,8]with ωðρÞ exchange. For the nonresonant η0→ γγη decay, the
VMD model is also used to generate the MC sample with ωð1420Þ or ρð1450Þ exchange. We use a sample of 1.225 × 109 simulated J=ψ events to study the backgrounds in
which the J=ψ decays generically (inclusive MC sample). The analysis is performed in the framework of the BESIII offline software systemwhich incorporates the detec-tor calibration, event reconstruction, and data sdetec-torage.
III. EVENT SELECTION AND BACKGROUND ESTIMATION
In the reconstruction of J=ψ → γη0 with η0→ γγη and η → γγ, candidate events must have no charged particle and at least five photons. Charged particles are identified by tracks in the active region of the MDC, corresponding to j cos θj < 0.93, where θ is the polar angle of the charged track with respect to the beam direction. They are also required to pass within10 cm of the interaction point in the beam direction and 1 cm of the beam line in the plane perpendicular to the beam. The photon candidate showers must have minimum energy of 25 MeV in the barrel region (j cos θj < 0.8) or 50 MeV in the end cap region (0.86 < j cos θj < 0.92). Showers in the region between the barrel and the end caps are poorly measured and excluded. A requirement of EMC cluster timing with respect to the most energetic photon (−500 ns < T < 500 ns) is used to suppress electronic noise and energy deposits unrelated to the event. To select J=ψ → γη0,η0→ γγη (η → γγ) signal events, only the events with exactly five photon candidates are selected, and the most energetic photon is taken as the radiative photon from the J=ψ decay. A four-constraint (4C) kinematic fit imposing energy-momentum conservation is performed to the γγγγγ hypothesis and theχ2 is required to be less than 200. To distinguish the photons from η0 and η decays, a variable δ2 η0η, defined as δ2η0η¼ ðMðγγηÞ−mðη 0Þ σ1 Þ 2þ ðMðγγÞ−mðηÞ σ2 Þ 2, is
introduced, where MðγγηÞ is the invariant mass of four of five selected photons (expect for the radiative photon) for reconstructing theη0meson, MðγγÞ is the invariant mass of photon pairs for reconstructing the η meson, while σ1¼ 11.7 MeV=c2 and σ
2¼ 9.7 MeV=c2 are the mass
reso-lutions of η0 and η, respectively, obtained from the MC simulations, mðη0Þ and mðηÞ are the η0 and η nominal masses, respectively. We then require jMðγγÞ − mðηÞj < 50 MeV=c2and the combination with the minimum value
ofδ2η0ηis chosen. Next theδ2η0ηis required to be less thanδ2ηη,
which is defined as δ2ηη ¼ ðM1ðγγÞ−mðηÞ
where M1ðγγÞ and M2ðγγÞ are the invariant masses of
arbitrary two of five selected photons, to suppress the background events from J=ψ → γηη.
To improve the mass resolution and further suppress background events, a five-constraint (5C) kinematic fit imposing energy-momentum conservation with a η mass constraint is performed under the γγγη hypothesis, where the η candidate is reconstructed with the pair of photons described above, and theχ25Cis required to be less than 30. The χ25C distribution is shown in Fig. 1. In addition, the invariant masses of all the two photon pairs are required not to be in the π0 mass region, jMðγγÞ − mðπ0Þj > 18 MeV=c2, to suppress the background events with π0
in the final state.
To remove the miscombinationed photon pairs in η candidates, the η decay angle θdecay, defined as the polar
angle of each photon in the correspondingγγ rest frame with respect to theη direction in the J=ψ rest frame, is required to satisfyj cos θdecayj < 0.95. An event is vetoed if any two of five selected photons (except for the combination for theη candidate) satisfyjMðγγÞ − mðηÞj < 35 MeV=c2.
The resultingγγη invariant mass distribution, after these requirements, is shown in Fig.2(a), where no significantη0 peak is observed. Detailed MC studies indicate that the background events accumulating near the lower side of the η0 signal region are mainly from J=ψ → γη0, η0→ π0π0η
(Class I), which is shown as the dotted (green) curve in Fig. 2(a). The peaking background is from J=ψ → γη0, η0→ γω, ω → γπ0, and is shown as the solid area in
Fig.2(a). The remaining background events are dominated by those J=ψ decays without η0in the final states (Class II), e.g., J=ψ → γηπ0 and J=ψ → ωη (ω → γπ0, η → γγ) decays. They constitute a smooth distribution in the η0 signal region as illustrated by the dashed (pink) curve in Fig.2(a).
IV. SIGNAL YIELD AND BRANCHING FRACTION An unbinned maximum likelihood fit to the MðγγηÞ distribution is performed to determine theη0→ γγη signal yield. In the fit, the probability density function (PDF) for the signal component is represented by the signal MC shape, which is obtained from the signal MC sample generated with an incoherent mixture of ρ, ω and the nonresonant components according to the fractions from the theoretical prediction [7,8]. The Class I and Class II background shapes are obtained from MC simulations and fixed, but the numbers are free parameters. Both the shape and the yield for the peaking background are fixed to the MC simulation and their expected intensities. The fit shown in Fig. 2(a) yields 24.9 10.3 η0 → γγη events with a statistical significance of2.6σ, and the branching fraction is calculated from
Bðη0→ γγηÞ ¼ Nobs
NJ=ψ·ε · Bðη → γγÞ · BðJ=ψ → γη0Þ
; ð1Þ where Nobs is the number of observed events determined
from the fit to the γγη mass spectrum, ε is the MC-determined detection efficiency, which is obtained from the signal MC sample described above; Bðη → γγÞ and BðJ=ψ → γη0Þ are the branching fractions of η → γγ and J=ψ → γη0 quoted from the PDG , respectively.
With the number of signal events and a detection efficiency of 11.4% the branching fraction is measured to be
Bðη0→ γγηÞ ¼ ð8.25 3.41 0.72Þ × 10−5; where the first uncertainty is statistical and the second systematic.
V. SYSTEMATIC UNCERTAINTIES
The systematic uncertainties on the upper limit meas-urement are summarized in TableI. The uncertainty due to the photon reconstruction is determined to be 0.5% per 5C 2 χ 0 50 100 150 200 Events/2.0 0 50 100 150 200 η’→γγη γπ0 , ωγ ω→ ’→ η Class I background Class II background Sum of background
FIG. 1. χ25Cdistributions in MC simulations and data. Dots with error bars are data, the wide (blue) solid-curve is the sum of expected backgrounds from MC simulations, the grid area is from signal MC with arbitrary normalization, the (green) dotted-curve is the Class I (J=ψ → γη0,η0→ π0π0η) background, the (pink) dashed-curve is the Class II (J=ψ → γηπ0 and J=ψ → ωη (ω → γπ0,η → γγ)) background, and solid area is the peaking background. ) 2 )(GeV/c γγη M( 0.8 0.9 1 1.1 1.2 ) 2 Events/(4MeV/c 0 10 20 30 40 Global fit →γγη ’ η Class I background Class II background 0 ω→γπ , ωγ ’ η → (a) ) γγη ’ η → N( 0 20 40 60 80 100
Normalized likehood value
0 0.2 0.4 0.6 0.8 1 (b)
FIG. 2. (a) Results of the fit to MðγγηÞ. The black dots with error bars are data, and the others are the results of the fit described in the text. (b) Likelihood distribution before (black dots) and after (blue squares) taking into account systematic uncertainties [see Eq.(2)]. The arrow is the position of the upper limit on the signal yields at 90% CL.
photon in the EMC barrel and 1.5% per photon in the EMC endcap. Thus the uncertainty associated with the five reconstructed photons is 3% (0.6% per photon) by weight-ing the uncertainties accordweight-ing to the polar angle distribu-tion of the five photons from data. The uncertainties associated with the other selection criteria, e.g., kinematic fit withχ25C< 30, the number of photons equal to 5, π0veto (jMðγγÞ − mðπ0Þj > 18 MeV=c2) and cosθdecay, are stud-ied using the J=ψ → γη0→ γγω, ω → γπ0 decay control sample . The systematic uncertainty for each of the applied selection criteria is numerically estimated from the difference of the number of events with and without the corresponding requirement. The resultant efficiency differences between data and MC simulations (2.7%, 0.5%, 1.9%, and 0.3%, respectively) are taken as the correspond-ing systematic uncertainties.
To suppress the multi-η backgrounds and remove the miscombinations of photons, an event is vetoed if any two of five selected photons (except for the combination for theη candidate) satisfy jMðγγÞ − mðηÞj < 35 MeV=c2. To estimate the systematic uncertainty, this requirement varied by10 MeV=c2, and the maximum change to the nominal result is taken as the systematic uncertainty.
The signal shape is obtained from the MC simulation in the nominal fit for theη0decay. The uncertainty due to the signal shape is considered by convolving a Gaussian function to account for the difference in the mass resolution between data and MC simulation. In the fit to the γγη distribution, the signal PDF is the signal MC shape convolving a Gaussian function with a fixed width of 1.5 MeV, and the changes of the signal yields is taken as the uncertainty due to the signal shape.
The uncertainty due to the Class I background and the peaking background are estimated by varying the numbers of expected background events by one standard deviation according to the uncertainties on the branching fractions values in PDG.
To take into account the systematic uncertainty due to signal model (VMD model), fits with alternative signal models for the different components, for example, a coherent sum for the ρ, ω-components and a uniform angular distribution in phase space for the nonresonant process is performed. The resultant changes in the branch-ing fractions (involvbranch-ing efficiency changes) are taken as the uncertainty related to the signal model.
To take into account the systematic uncertainties asso-ciated with the fit of the mass spectrum coming from the background events and the fit range, alternative fits with different fit ranges, background shapes and the number of background events are performed. The largest number of the signal yield among these cases is chosen to calculate the upper limit of the branching fraction at the 90% CL.
The number of J=ψ events is NJ=ψ ¼ ð1310.6 7.0Þ ×
106 , corresponding to an uncertainty of 0.5%. The
branching fractions for the J=ψ → γη0 andη → γγ decays are taken from the PDG , and the corresponding uncertainties are taken as a systematic uncertainty.
Assuming all systematic uncertainties in Table I are independent, the total systematic uncertainty, obtained from their quadratic sum, is 8.7%.
VI. η0→ γγη UPPER LIMIT RESULTS
Since no significantη0peak is seen, we use the Bayesian method to obtain the signal upper limit. Unbinned maxi-mum likelihood fits are performed on the γγη mass spectrum with a series of input signal events, and the distribution of normalized likelihood values is taken as the PDF for the expected number of events.
The final upper limit on the branching fraction is determined by convolving the normalized likelihood curve LðNÞ with the systematic uncertainties as a Gaussian function [Gðμ; σÞ ¼ Gð0; σsysÞ] to obtain the smeared
like-lihood L0ðN0Þ, which is written as L0ðN0Þ ¼ Z ∞ 0 LðNÞ 1 ﬃﬃﬃﬃﬃﬃ 2π p σsys exp −ðN0− NÞ2 2σ2 sys dN; ð2Þ
whereσsys¼ N · σrel, N and σrel are the input signal yield
and the corresponding uncertainty, respectively. Figure2(b) shows the likelihood distribution before and after convolv-ing the Gaussian function. The upper limit on the number of η0→ γγη events, N0UL, is determined to be 40 at the 90% CL. The corresponding upper limit on the branching fraction of η0→ γγη is determined to be Bðη0→ γγηÞ < 1.33 × 10−4 at the 90% CL.
With a data sample of 1.31 × 109J=ψ events collected with the BESIII detector, we report on a search for the doubly radiative decay η0→ γγη for the first time, where theη0meson is produced via the J=ψ → γη0process.
TABLE I. Summary of relative systematic uncertainties for the upper limit on the branching fraction measurement (in %).
Source Systematic uncertainties
Photon detection 3.0 Kinematic fit (5C) 2.7 Number of photonsðNγ¼ 5Þ 0.5 π0 andγ veto 1.9 cosθdecay 0.3 η veto 4.3 Signal shape 3.2 Class I background 3.1 Peaking background 0.8 Signal model 2.9
Cited branching fractions 3.3
Number of J=ψ events 0.5
The observed signal yields in the γγη invariant mass spectrum corresponds to 2.6σ, this signal corresponds to a branching fraction of ð8.25 3.41 0.72Þ × 10−5. We also present an upper limit of the branching fraction of 1.33 × 10−4 at the 90% CL. The obtained result is in
tension with a recent theoretical prediction of 2.0 × 10−4  within the frame work of the linear σ model and the VMD model.
The BESIII collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; National Natural Science Foundation of China (NSFC)
under Contracts No. 11625523, No. 11635010,
No. 11675184, No. 11735014, No. 11835012; the
Chinese Academy of Sciences (CAS) Large-Scale
Scientific Facility Program; Joint Large-Scale Scientific Facility Funds of the NSFC and CAS under Contracts
No. U1532257, No. U1532258, No. U1732263,
No. U1832207; CAS Key Research Program of Frontier Sciences under Contracts No. QYZDJ-SSW-SLH003, No. QYZDJ-SSW-SLH040; 100 Talents Program of CAS; INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG under Contracts No. Collaborative Research Center CRC 1044, FOR 2359; Istituto Nazionale di Fisica Nucleare, Italy; Koninklijke Nederlandse Akademie van
Wetenschappen (KNAW) under Contract No.
530-4CDP03; Ministry of Development of Turkey under Contract No. DPT2006K-120470; National Science and Technology fund; The Knut and Alice Wallenberg Foundation (Sweden) under Contract No. 2016.0157; The Royal Society, UK under Contract No. DH160214; The Swedish Research Council; U.S. Department of
Energy under Contracts No. DE-FG02-05ER41374,
No. DE-SC-0010118, No. DE-SC-0012069; University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt.
 J. Steinberger, Phys. Rev. 76, 1180 (1949); S. L. Adler, Phys. Rev. 177, 2426 (1969); J. S. Bell and R. Jackiw, Nuovo Cimento A 60, 47 (1969); W. A. Bardeen,Phys. Rev. 184, 1848 (1969).
 J. Wess and B. Zumino,Phys. Lett. 37B, 95 (1971).  E. Witten,Nucl. Phys. B223, 422 (1983).
 H. B. Li,J. Phys. G 36, 085009 (2009).
 A. Kupsc,Int. J. Mod. Phys. E 18, 1255 (2009).
 J. Gasser and H. Leutwyler,Nucl. Phys. B250, 465 (1985); H. Neufeld and H. Rupertsberger,Z. Phys. C 68, 91 (1995).  R. Jora, Nucl. Phys. B, Proc. Suppl. 207, 224 (2010).  R. Escribano et al.,arXiv:1812.08454.
 M. Ablikim et al. (BESIII Collaboration),Phys. Rev. D 96, 012005 (2017).
 S. V. Donskov, V. N. Kolosov, A. A. Lednev, Y. V. Mikhailov, V. A. Polyakov, V. D. Samoylenko, and G. V. Khaustov,Phys. At. Nucl. 78, 1043 (2015).
 M. Ablikim et al. (BESIII Collaboration),Phys. Rev. D 97, 012003 (2018).
 M. Ablikim et al. (BESIII Collaboration),Phys. Rev. Lett. 120, 242003 (2018).
 M. Ablikim et al. (BESIII Collaboration),Phys. Rev. D 92, 012014 (2015).
 M. Ablikim et al. (BESIII Collaboration),Phys. Rev. Lett. 118, 012001 (2017).
 M. Ablikim et al. (BESIII Collaboration),Phys. Rev. D 92, 012001 (2015).
 M. Ablikim et al. (BESIII Collaboration),Phys. Rev. D 87, 092011 (2013).
 M. Ablikim et al. (BESIII Collaboration),Phys. Rev. Lett. 112, 251801 (2014).
 M. Ablikim et al. (BESIII Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 614, 345 (2010).
 C. H. Yu et al., Proceedings of IPAC2016, Busan, Korea (2016), https://dx.doi.org/10.18429/JACoW-IPAC2016-TUYA01.
 S. Agostinelli et al. (GEANT4 Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 506, 250 (2003).  Z. Y. Deng et al., Chin. Phys. C 30, 371 (2006).
 S. Jadach, B. F. L. Ward, and Z. Was, Comput. Phys. Commun. 130, 260 (2000);Phys. Rev. D 63, 113009 (2001).  D. J. Lange, Nucl. Instrum. Methods Phys. Res., Sect. A 462, 152 (2001); R. G. Ping,Chin. Phys. C 32, 599 (2008).  M. Tanabashi et al. (Particle Data Group),Phys. Rev. D 98,
 J. C. Chen, G. S. Huang, X. R. Qi, D. H. Zhang, and Y. S. Zhu,Phys. Rev. D 62, 034003 (2000).
 W. D. Li et al., in Proceeding of CHEP06, Mumbai, India, 2006, edited by Sunanda Banerjee (Tata Institute of Funda-mental Research, Mumbai, 2006).
 M. Ablikim et al. (BESIII Collaboration),Phys. Rev. D 96, 112012 (2017).
 M. Ablikim et al. (BESIII Collaboration),Chin. Phys. C 41, 013001 (2017).